Question

Match the following equations to its equivalent below
Y = x^2 - 10x + 16, y = (x+3)^2 - 8, y = (x+9)(x+1), y = x^2 + 2x - 8.
Equivalents: y = x^2 + 6x + 1, y = (x-2)(x-8), y = x^2 + 10x + 9, y = (x + 1)^2 - 9

Answer 1

To match the given equations with their equivalents, we'll first rewrite and simplify each of the provided equations and the equivalents where necessary.

1. **For** \( Y = x^2 - 10x + 16 \):
- This can be factored as follows:
\[
Y = (x - 2)(x - 8)
\]
So, it matches with \( y = (x-2)(x-8) \).

2. **For** \( y = (x + 3)^2 - 8 \):
- Expanding the square:
\[
y = (x^2 + 6x + 9) - 8 = x^2 + 6x + 1
\]
So, it matches with \( y = x^2 + 6x + 1 \).

3. **For** \( y = (x + 9)(x + 1) \):
- Expanding this:
\[
y = x^2 + 10x + 9
\]
So, it matches with \( y = x^2 + 10x + 9 \).

4. **For** \( y = x^2 + 2x - 8 \):
- This can be rewritten and completed to find the equivalent in vertex form:
\[
y = (x + 1)^2 - 9
\]
So, it matches with \( y = (x + 1)^2 - 9 \).

Thus, the matches are:

- \( Y = x^2 - 10x + 16 \) ↔ \( y = (x-2)(x-8) \)
- \( y = (x + 3)^2 - 8 \) ↔ \( y = x^2 + 6x + 1 \)
- \( y = (x + 9)(x + 1) \) ↔ \( y = x^2 + 10x + 9 \)
- \( y = x^2 + 2x - 8 \) ↔ \( y = (x + 1)^2 - 9 \)